Systems of parallel lines have no solution. Pupils work examples to discover that lines with the same slope and different y-intercepts are parallel. The 27th segment of 33 uses this discovery to develop a proof, and the class determines...

Explore angle relationships associated with transversals. Pupils construct parallel lines with a transversal and find the measures of the angles formed. They figure out how the different angles are related before constructing...

Challenge the class to prove that the dilation properties always hold. The lesson develops an informal proof of the properties of dilations through a discussion. Two of the proofs are verified with each class member performing the...

What does it take to show two triangles are similar? The 11th segment in a series of 16 introduces the AA Criterion for Similarity. A discussion provides an informal proof of the theorem. Exercises and problems require scholars to apply...

Given a pair of parallel lines and a triangle in between, geometers prove that the sum of the interior angles is 180 degrees. This quick quest can be used as a pop quiz or exit ticket for your geometry class.

What figure is formed by connecting the midpoints of the sides of a quadrilateral? The geometry assessment task has class members work through the process of determining the figure inscribed in a quadrilateral. Pupils use geometric...

Challenge the class with inscribed circles in triangles. The assessment task requests class members use their knowledge of circles and right triangles to prove two triangles are congruent. They go on to utilize their knowledge of...

High School geometers verify through experimentation certain properties about dilations. This multi-step problem challenges them to construct examples of dilations to verify specific facts, the final step provides an opportunity to more...

This task asks learners to prove that the segment joining the midpoints of two sides of a parallelogram is both congruent and parallel to an adjacent side of the parallelogram. The activity would be good to use in a discussion about how...

If both pairs of opposite sides of a quadrilateral are congruent, is the quadrilateral a parallelogram? This task asks learners to determine the answer and to support their answer with a proof. The resource includes a commentary for...

Challenge: create an assessment that features higher level thinking from beginning to end. A ready-made test assesses knowledge of dilations using performance tasks. Every question requires a developed written response. 

Determine whether two triangles are similar. The lesson presents opportunities for pupils to find the criterion needed to show that two triangles are similar. Scholars use the definition of similarity to find any missing side...